Regular Article – Theoretical Physics
Two-point function of the energy-momentum tensor and generalised conformal structure
INFN-Lecce and Dipartimento di Matematica e Fisica, Università del Salento, Via Arnesano, 73100, Lecce, Italy
2 INFN, Sezione di Firenze and Department of Physics and Astronomy, University of Florence, Via G. Sansone 1, 50019, Sesto Fiorentino, Italy
3 STAG Research Centre and Mathematical Sciences, Highfield, University of Southampton, SO17 1BJ, Southampton, UK
Accepted: 18 January 2021
Published online: 21 February 2021
Theories with generalised conformal structure contain a dimensionful parameter, which appears as an overall multiplicative factor in the action. Examples of such theories are gauge theories coupled to massless scalars and fermions with Yukawa interactions and quartic couplings for the scalars in spacetime dimensions other than 4. Many properties of such theories are similar to that of conformal field theories (CFT), and in particular their 2-point functions take the same form as in CFT but with the normalisation constant now replaced by a function of the effective dimensionless coupling g constructed from the dimensionful parameter and the distance separating the two operators. Such theories appear in holographic dualities involving non-conformal branes and this behaviour of the correlators has already been observed at strong coupling. Here we present a perturbative computation of the two-point function of the energy-momentum tensor to two loops in dimensions , confirming the expected structure and determining the corresponding functions of g to this order, including the effects of renormalisation. We also discuss the case for comparison. The results for are relevant for holographic cosmology, and in this case we also study the effect of a coupling, which while marginal in the usual sense it is irrelevant from the perspective of the generalised conformal structure. Indeed, the effect of such coupling in the 2-point function is washed out in the IR but it modifies the UV.
© The Author(s) 2021
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